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作者：Kontoyiannis, I.; Meyn, S. P.
作者单位：Athens University of Economics & Business; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We argue that the spectral theory of non-reversible Markov chains may often be more effectively cast within the framework of the naturally associated weighted-L (a) space , instead of the usual Hilbert space L (2) = L (2)(pi), where pi is the invariant measure of the chain. This observation is, in part, based on the following results. A discrete-time Markov chain with values in a general state space is geometrically ergodic if and only if its transition kernel admits a spectral gap in . If the...
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作者：Freidlin, M. I.; Wentzell, A. D.
作者单位：University System of Maryland; University of Maryland College Park; Tulane University
摘要：The diffusion process in a region G subset of R-2 governed by the operator (L) over tilde (epsilon) = 1/2u(xx) + 1/2 epsilon u(zz) inside the region and undergoing instantaneous co-normal reflection at the boundary is considered. We show that the slow component of this process converges to a diffusion process on a certain graph corresponding to the problem. This allows to find the main term of the asymptotics for the solution of the corresponding Neumann problem in G. The operator (L) over til...
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作者：Gloria, Antoine; Mourrat, Jean-Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille; Aix-Marseille Universite
摘要：This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation formula to design and analyze effective and computable approximations of the homogenized coefficients. In particular, we show that information on the edge of the spectrum of the generator of the environment viewed by the particle projected on the local drift yiel...
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作者：Grigorescu, Ilie; Kang, Min
作者单位：University of Miami; North Carolina State University
摘要：We study the existence and asymptotic properties of a conservative branching particle system driven by a diffusion with smooth coefficients for which birth and death are triggered by contact with a set. Sufficient conditions for the process to be non-explosive are given. In the Brownian motions case the domain of evolution can be non-smooth, including Lipschitz, with integrable Martin kernel. The results are valid for an arbitrary number of particles and non-uniform redistribution after branch...
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作者：Fleury, B.
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：Let K-N = [+/- G1, ...., +/- G(N)] be the absolute convex hull of N independent standardGaussian random points in R-n with N >= n. We prove that, for any 1- Lipschitz function f : R-n -> R, the polytope K-N satisfies the following Poincare inequality in mean value: E-omega integral(KN(omega))(f (x) - 1/vol(n) (K-N (omega))integral(KN(omega)) f (y)dy)(2) dx <= C/n E-omega integral(KN(omega)) |x|(2)dx where C > 0 is an absolute constant. This Poincare inequality is the one suggested by a conject...
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作者：DeBlassie, Dante
作者单位：New Mexico State University
摘要：We determine precise logarithmic asymptotics of the probability of a large exit time for Brownian motion in a quasi-cone. This answers a question formally posed by Lifshits and Shi (Bernoulli 8:745-765, 2002), but first studied by Li (Ann Probab 31:1078-1096, 2001).
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作者：Coquille, Loren; Velenik, Yvan
作者单位：University of Geneva
摘要：In the late 1970s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs measures of the two-dimensional ferromagnetic nearest-neighbor Ising model at inverse temperature are of the form , where and are the two pure phases and . We present here a new approach to this result, with a number of advantages: (a) We obtain an optimal finite-volume, quantitative analogue (implying the classical claim); (b) the scheme of our proof seems more natural an...
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作者：Durand, Arnaud; Jaffard, Stephane
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We study the pointwise regularity properties of the L,vy fields introduced by T. Mori; these fields are the most natural generalization of L,vy processes to the multivariate setting. We determine their spectrum of singularities, and we show that their Holder singularity sets satisfy a large intersection property in the sense of K. Falconer.
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作者：Bieniek, Mariusz; Burdzy, Krzysztof; Finch, Sam
作者单位：University of Washington; University of Washington Seattle; Maria Curie-Sklodowska University; Aarhus University
摘要：We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until one of them hits the boundary. This particle is killed but another randomly chosen particle branches into two particles, to keep the population size constant. We prove that the particle population does not approach the boundary simultaneously in a finite time in some Lipschitz domains. This is used to prove a limit t...
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作者：Kerkyacharian, Gerard; Nickl, Richard; Picard, Dominique
作者单位：University of Cambridge; Universite Paris Cite; Sorbonne Universite
摘要：Let X (1), . . . , X (n) be a random sample from some unknown probability density f defined on a compact homogeneous manifold M of dimension d a parts per thousand yen 1. Consider a 'needlet frame' describing a localised projection onto the space of eigenfunctions of the Laplace operator on M with corresponding eigenvalues less than 2(2j) , as constructed in Geller and Pesenson (J Geom Anal 2011). We prove non-asymptotic concentration inequalities for the uniform deviations of the linear needl...
